F3.8 · Explain step-up and step-down transformer operation

Ontario Grade 11 Physics

Electricity and Magnetism

Ontario Grade 11 Physics — F3.8

What you will learn

• Describe the main parts of a transformer and the role of changing current.
• Use the turns ratio to compare primary and secondary voltage.
• Explain how current changes in an ideal step-up or step-down transformer.
• Check whether a calculated transformer result makes physical sense.

1. The system and the needed ideas

• Primary means input; secondary means output.
• A continuing change in current and magnetic field is needed.
• The core guides the changing magnetic field between the coils.

2. Turns ratio and voltage change

• More secondary turns means a higher secondary voltage.
• Fewer secondary turns means a lower secondary voltage.
• Use voltage magnitudes with the stated input-output labels.

3. Current change and a useful check

• For an ideal transformer, input power equals output power.
• A voltage increase pairs with a current decrease.
• Check that current changes in the opposite sense to voltage.

Worked example

Finding the output voltage of a step-up transformer

1. Set up the system
   The transformer coils are the system. Treat voltage as a positive magnitude, with the primary as input and the secondary as output. The known values are $N_p=400$, $N_s=1600$, and $V_p=12\,\mathrm{V}$. The unknown is $V_s$.
2. Apply the turns ratio
   For an ideal transformer, secondary voltage divided by primary voltage equals secondary turns divided by primary turns. Rearrange to find the output voltage.
   $$V_s=V_p\frac{N_s}{N_p}$$
3. Substitute and calculate
   The turns ratio is four, so the output voltage is four times the input voltage. Keep the voltage unit in the calculation.
   $$V_s=(12\,\mathrm{V})\frac{1600}{400}=48\,\mathrm{V}$$

Worked example

Finding turns in a step-down transformer

1. Define the quantities
   The transformer coils are the system. Use positive voltage magnitudes, with the primary as input and secondary as output. The known values are $N_p=900$, $V_p=120\,\mathrm{V}$, and $V_s=24\,\mathrm{V}$. The unknown is $N_s$.
2. Rearrange the model
   The voltage ratio equals the turns ratio. Multiply the primary turns by the secondary-to-primary voltage ratio to find the secondary turns.
   $$N_s=N_p\frac{V_s}{V_p}$$
3. Substitute and calculate
   The output voltage is one-fifth of the input voltage, so the secondary has one-fifth as many turns as the primary.
   $$N_s=(900)\frac{24\,\mathrm{V}}{120\,\mathrm{V}}=180$$

Worked example

Finding output current in an ideal step-down transformer

1. Identify the system and values
   The transformer is the system. Treat current and voltage as positive magnitudes. The primary is input and the secondary is output. The known values are $V_p=240\,\mathrm{V}$, $V_s=60\,\mathrm{V}$, and $I_p=0.50\,\mathrm{A}$. The unknown is $I_s$.
2. Use ideal power transfer
   For an ideal transformer, input power equals output power. Since power is voltage multiplied by current, rearrange to find the secondary current.
   $$I_s=\frac{V_p I_p}{V_s}$$
3. Substitute and calculate
   Use volts and amperes throughout. The voltage drops by a factor of four, so the current rises by that factor in the ideal model.
   $$I_s=\frac{(240\,\mathrm{V})(0.50\,\mathrm{A})}{60\,\mathrm{V}}=2.0\,\mathrm{A}$$

Common mistakes and how to avoid them

Lesson summary

• A changing primary current creates a changing magnetic field that induces voltage in the secondary coil.
• The voltage ratio equals the turns ratio for an ideal transformer.
• More secondary turns give a step-up transformer; fewer give a step-down transformer.
• In the ideal model, voltage and current change in opposite senses, while input and output power are equal.
• Check labels, units, significant figures, and whether the result matches step-up or step-down operation.

Check your understanding

Key terms

Alternating current (AC)

Electric current that repeatedly changes size and direction.

Primary coil

The transformer coil connected to the input.

Secondary coil

The transformer coil that provides the output.

Turn

One loop of wire in a coil.

Electromagnetic induction

The production of voltage by a changing magnetic field.

Ideal transformer

A simplified transformer model in which energy losses are negligible.

Step-up transformer

A transformer whose secondary voltage is greater than its primary voltage.

Step-down transformer

A transformer whose secondary voltage is less than its primary voltage.

Continue through SPH3U

View the complete SPH3U Ontario Grade 11 Physics curriculum and lessons

• F1.1 · Analyse social and economic impacts of electromagnetic technologies
• F1.2 · Assess electrical generation efficiency and sustainability
• F2.1 · Use terminology for current, voltage, resistance, power, and transformers
• F2.2 · Analyse series, parallel, and mixed circuits with Ohm’s and Kirchhoff’s laws
• F2.3 · Design and explain mixed direct-current circuits
• F2.4 · Investigate properties of magnetic fields

About this lesson and its review

Published by DoAssignment. This AI-assisted lesson follows Ontario Grade 11 Physics (SPH3U), expectation F3.8. It is a study resource, not an official curriculum publication.

Before publication, the draft is checked for structure, mathematical or chemical notation, calculations, course boundaries, and readability, and then requires administrator approval. Errors can still occur, so corrections are welcomed.

Official curriculum reference

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